Privacy preserving data aggregating with multiple access channel

We consider the scenario in which a set of users want to compute an aggregate function of their messages at a message center. The users communicate with the message center over a multiple access channel with fading, where the fading states of the channels from individual receivers are unknown a priori to the message center. For privacy reasons, the users do not want disclose their message information to the message center. No computational limitations on the message center are assumed, and the message center may collude with a set of hidden eavesdroppers to retrieve the message information of the users. This paper proposes a scheme called MacPDA that leverages the multiple access properties of wireless signals to achieve privacy. It relies on fairly loose synchronization and does not require secret channels. MacPDA is shown to reveal no message information of the users other than the required function value. The estimation performance of MacPDA is investigated with numerical experiments, and theoretical bounds are given on the asymptotic performance.